Phase-integral calculation of quantal matrix elements of exp{−ax} between unbound states in the one-dimensional potential C exp{−ax}

✍ Scribed by P.O Fröman; A Hökback; E Walles; S Yngve

• Publisher: Elsevier Science
• Year: 1985
• Tongue: English
• Weight: 551 KB
• Volume: 163
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(85)90381-1

✦ Synopsis

In order to obtain further information on the accuracy of phase-integral formulas for calculating quanta1 expectation values and matrix elements involving unbound states, without the use of wavefunctions, the formulas are applied to an exactly soluble one-dimensional model. In this model the potential is proportional to exp{ -ax}, where a is a positive constant and x is a variable ranging from -co to + co, and expectation values as well as matrix elements of the function exp{ -ax} are considered. When the phase-integral results are compared with the exact results, the very satisfactory nature of the phase-integral formulas is further established.